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# Counting

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How many rectangles are in this figure? Each angle is a right angle. Jan 24, 2022

#1
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Count it by shape:

length x width

1 x 1: 12

1 x 2: 9

1 x 3: 6

1 x 4: 3

2 x 1: 8

2 x 2: 6

2 x 3: 4

2 x 4: 2

3 x 1: 4

3 x 2: 3

3 x 3: 2

3 x 4: 1

Add everything up, and you get 60.

Jan 24, 2022
#2
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If you consider the "squares" as rectangles, then we can count the number of rectangle sizes there are.

For the size 1x1 there are 12 squares/rectangles.

For the next size which is a 2 x 1, there are 17 rectangles.

For the next size which is a 3 x 1, there are 10 of those rectangles.

For the next size which is a 4 x 1, there are 3 of those rectangles.

For the next size which is a 2 x 2, there are 6 of those squares/rectangles.

For the next size which is 2 x 3, there are 7 of those rectangles.

For the next size which is 2 x 4, there are 2 of those rectangles.

For the next size which is 3 x 4, there is 1 rectangle.

For the last size which is 3 x 3, there are 2 of those squares/rectangles.

Altogether there are 40 rectangles and 20 squares. (You might count squares as rectangles.) Jan 24, 2022